OK, let me try saying this another way. Yes, indeed if you just run one ground wire between three different turntables and preamps, all connected together, the voltage differences in that single conductor can cause significant problems.
Attempting to find the "magic" quiet point to connect sundry circuits is one part wishful thinking and a rejection of basic engineering principles. Your difficulty trying to do this is not surprising. It is very likely impossible to do, and quiet today, may be noisy tomorrow if some external factor changes.
There is a method to manage different ground potentials, namely use of differential circuitry. A signal is treated as (signal +)-(signal -). This maintains signal integrity. Note ground can not be hard bonded to signal- at both ends of a span.
Warning- I'm about to repeat myself again, but I'll change it a little to keep it interesting for myself.
Instead of thinking of one ground, lets give "them" cute names; RIAA gnd 1,2,3, chassis/ps gnd, turntable gnd 1,2,3. And non grounds, Cart L, R, +, -, 1,2,3.
The bottom of your 1000uf gain cap in preamp 1 connects hard to RIAA gnd 1, 2 to 2, 3 to 3. The phono cart, L & R - also connect to these RIAA gnds respectively (but not each other.
We will now have clean uncorrupted RIAA equalized signals at the output of these 3 different RIAA stages, but this clean signal is relative to or reference to these 3 RIAA gnds. The task now is how to reference these 3 grounds to a common PS gnd, chassis ground, and to following equipment. It is possible that you might be able to hard bond these 3 RIAA gnds directly to the PS gnd, but I would be nervous about potential loops so would connect through a small compliance (say 10 ohms and .1uF).
Now the final remaining issue is getting the clean signal out of your box. If the following equipment is balanced or true differential input (+,-,and gnd) you could simply connect output + to each RIAA output, output - to each RIAA gnd, and output gnd to PS/chassis ground. For stability and balance I would use 50-100 ohms build out resistors in series with each + and - output.
If you need to output a 2 circuit unbalanced signal referenced to a common chassis ground you will need 3 more differential amplifiers (1 each opamp w/4 resistors) to reference between the RIAA gnds and the common output ground (or perhaps the following product's unbalanced input -/gnd).
Final housekeeping is that turntables should be hard grounded to chassis ground and hopefully turntable gnds are isolated from tone arm wiring.
I hope this finally makes sense. If you think it's difficult making three phonos play nice together, try putting 40 mic preamps in a single chassis..
JR
Note: in a single preamp it is probably possible to bond the RIAA gnd to the chassis gnd at the unbalanced output and get away with it. The combination of 3 different preamps confounds this simpler grounding scheme.